Search Results for author: Alain Durmus

Found 30 papers, 10 papers with code

On Maximum-a-Posteriori estimation with Plug & Play priors and stochastic gradient descent

no code implementations16 Jan 2022 Rémi Laumont, Valentin De Bortoli, Andrés Almansa, Julie Delon, Alain Durmus, Marcelo Pereyra

Bayesian methods to solve imaging inverse problems usually combine an explicit data likelihood function with a prior distribution that explicitly models expected properties of the solution.

Image Denoising

NEO: Non Equilibrium Sampling on the Orbits of a Deterministic Transform

1 code implementation NeurIPS 2021 Achille Thin, Yazid Janati El Idrissi, Sylvain Le Corff, Charles Ollion, Eric Moulines, Arnaud Doucet, Alain Durmus, Christian Robert

Sampling from a complex distribution $\pi$ and approximating its intractable normalizing constant $\mathrm{Z}$ are challenging problems.

Asymptotic bias of inexact Markov Chain Monte Carlo methods in high dimension

no code implementations2 Aug 2021 Alain Durmus, Andreas Eberle

As a consequence, the same dependence on the step size and the dimension as in the product case can be recovered for several important classes of models.

Monte Carlo Variational Auto-Encoders

1 code implementation30 Jun 2021 Achille Thin, Nikita Kotelevskii, Arnaud Doucet, Alain Durmus, Eric Moulines, Maxim Panov

Variational auto-encoders (VAE) are popular deep latent variable models which are trained by maximizing an Evidence Lower Bound (ELBO).

Fast Approximation of the Sliced-Wasserstein Distance Using Concentration of Random Projections

1 code implementation NeurIPS 2021 Kimia Nadjahi, Alain Durmus, Pierre E. Jacob, Roland Badeau, Umut Şimşekli

The Sliced-Wasserstein distance (SW) is being increasingly used in machine learning applications as an alternative to the Wasserstein distance and offers significant computational and statistical benefits.

DG-LMC: A Turn-key and Scalable Synchronous Distributed MCMC Algorithm via Langevin Monte Carlo within Gibbs

no code implementations11 Jun 2021 Vincent Plassier, Maxime Vono, Alain Durmus, Eric Moulines

Performing reliable Bayesian inference on a big data scale is becoming a keystone in the modern era of machine learning.

Bayesian Inference

Tight High Probability Bounds for Linear Stochastic Approximation with Fixed Stepsize

no code implementations NeurIPS 2021 Alain Durmus, Eric Moulines, Alexey Naumov, Sergey Samsonov, Kevin Scaman, Hoi-To Wai

This family of methods arises in many machine learning tasks and is used to obtain approximate solutions of a linear system $\bar{A}\theta = \bar{b}$ for which $\bar{A}$ and $\bar{b}$ can only be accessed through random estimates $\{({\bf A}_n, {\bf b}_n): n \in \mathbb{N}^*\}$.

QLSD: Quantised Langevin stochastic dynamics for Bayesian federated learning

no code implementations1 Jun 2021 Maxime Vono, Vincent Plassier, Alain Durmus, Aymeric Dieuleveut, Eric Moulines

The objective of Federated Learning (FL) is to perform statistical inference for data which are decentralised and stored locally on networked clients.

Federated Learning

NEO: Non Equilibrium Sampling on the Orbit of a Deterministic Transform

1 code implementation17 Mar 2021 Achille Thin, Yazid Janati, Sylvain Le Corff, Charles Ollion, Arnaud Doucet, Alain Durmus, Eric Moulines, Christian Robert

Sampling from a complex distribution $\pi$ and approximating its intractable normalizing constant Z are challenging problems.

Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie

no code implementations8 Mar 2021 Rémi Laumont, Valentin De Bortoli, Andrés Almansa, Julie Delon, Alain Durmus, Marcelo Pereyra

The proposed algorithms are demonstrated on several canonical problems such as image deblurring, inpainting, and denoising, where they are used for point estimation as well as for uncertainty visualisation and quantification.

Bayesian Inference Deblurring +2

On Riemannian Stochastic Approximation Schemes with Fixed Step-Size

no code implementations15 Feb 2021 Alain Durmus, Pablo Jiménez, Éric Moulines, Salem Said

This result gives rise to a family of stationary distributions indexed by the step-size, which is further shown to converge to a Dirac measure, concentrated at the solution of the problem at hand, as the step-size goes to 0.

Nonreversible MCMC from conditional invertible transforms: a complete recipe with convergence guarantees

no code implementations31 Dec 2020 Achille Thin, Nikita Kotelevskii, Christophe Andrieu, Alain Durmus, Eric Moulines, Maxim Panov

This paper fills the gap by developing general tools to ensure that a class of nonreversible Markov kernels, possibly relying on complex transforms, has the desired invariance property and leads to convergent algorithms.

Quantitative Propagation of Chaos for SGD in Wide Neural Networks

no code implementations NeurIPS 2020 Valentin De Bortoli, Alain Durmus, Xavier Fontaine, Umut Simsekli

In comparison to previous works on the subject, we consider settings in which the sequence of stepsizes in SGD can potentially depend on the number of neurons and the iterations.

Convergence Analysis of Riemannian Stochastic Approximation Schemes

no code implementations27 May 2020 Alain Durmus, Pablo Jiménez, Éric Moulines, Salem Said, Hoi-To Wai

This paper analyzes the convergence for a large class of Riemannian stochastic approximation (SA) schemes, which aim at tackling stochastic optimization problems.

Stochastic Optimization

Convergence rates and approximation results for SGD and its continuous-time counterpart

no code implementations8 Apr 2020 Xavier Fontaine, Valentin De Bortoli, Alain Durmus

This paper proposes a thorough theoretical analysis of Stochastic Gradient Descent (SGD) with non-increasing step sizes.

Stochastic Optimization

Statistical and Topological Properties of Sliced Probability Divergences

1 code implementation NeurIPS 2020 Kimia Nadjahi, Alain Durmus, Lénaïc Chizat, Soheil Kolouri, Shahin Shahrampour, Umut Şimşekli

The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base divergence' between one-dimensional random projections of the two measures.

Maximum likelihood estimation of regularisation parameters in high-dimensional inverse problems: an empirical Bayesian approach. Part I: Methodology and Experiments

1 code implementation26 Nov 2019 Ana F. Vidal, Valentin De Bortoli, Marcelo Pereyra, Alain Durmus

In this work, we propose a general empirical Bayesian method for setting regularisation parameters in imaging problems that are convex w. r. t.

Methodology Computation 62C12, 65C40, 68U10, 62F15, 65J20, 65C60, 65J22

Approximate Bayesian Computation with the Sliced-Wasserstein Distance

1 code implementation28 Oct 2019 Kimia Nadjahi, Valentin De Bortoli, Alain Durmus, Roland Badeau, Umut Şimşekli

Approximate Bayesian Computation (ABC) is a popular method for approximate inference in generative models with intractable but easy-to-sample likelihood.

Image Denoising

Markov Decision Process for MOOC users behavioral inference

no code implementations10 Jul 2019 Firas Jarboui, Célya Gruson-daniel, Pierre Chanial, Alain Durmus, Vincent Rocchisani, Sophie-helene Goulet Ebongue, Anneliese Depoux, Wilfried Kirschenmann, Vianney Perchet

Studies on massive open online courses (MOOCs) users discuss the existence of typical profiles and their impact on the learning process of the students.

Asymptotic Guarantees for Learning Generative Models with the Sliced-Wasserstein Distance

1 code implementation NeurIPS 2019 Kimia Nadjahi, Alain Durmus, Umut Şimşekli, Roland Badeau

Minimum expected distance estimation (MEDE) algorithms have been widely used for probabilistic models with intractable likelihood functions and they have become increasingly popular due to their use in implicit generative modeling (e. g. Wasserstein generative adversarial networks, Wasserstein autoencoders).

Copula-like Variational Inference

1 code implementation NeurIPS 2019 Marcel Hirt, Petros Dellaportas, Alain Durmus

This family is based on new copula-like densities on the hypercube with non-uniform marginals which can be sampled efficiently, i. e. with a complexity linear in the dimension of state space.

Variational Inference

The promises and pitfalls of Stochastic Gradient Langevin Dynamics

no code implementations NeurIPS 2018 Nicolas Brosse, Alain Durmus, Eric Moulines

As $N$ becomes large, we show that the SGLD algorithm has an invariant probability measure which significantly departs from the target posterior and behaves like Stochastic Gradient Descent (SGD).

Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusions

1 code implementation21 Jun 2018 Antoine Liutkus, Umut Şimşekli, Szymon Majewski, Alain Durmus, Fabian-Robert Stöter

To the best of our knowledge, the proposed algorithm is the first nonparametric IGM algorithm with explicit theoretical guarantees.

Bridging the Gap between Constant Step Size Stochastic Gradient Descent and Markov Chains

no code implementations20 Jul 2017 Aymeric Dieuleveut, Alain Durmus, Francis Bach

We consider the minimization of an objective function given access to unbiased estimates of its gradient through stochastic gradient descent (SGD) with constant step-size.

Stochastic Gradient Richardson-Romberg Markov Chain Monte Carlo

no code implementations NeurIPS 2016 Alain Durmus, Umut Simsekli, Eric Moulines, Roland Badeau, Gaël Richard

We illustrate our framework on the popular Stochastic Gradient Langevin Dynamics (SGLD) algorithm and propose a novel SG-MCMC algorithm referred to as Stochastic Gradient Richardson-Romberg Langevin Dynamics (SGRRLD).

Bayesian Inference

High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm

no code implementations5 May 2016 Alain Durmus, Eric Moulines

We consider in this paper the problem of sampling a high-dimensional probability distribution $\pi$ having a density with respect to the Lebesgue measure on $\mathbb{R}^d$, known up to a normalization constant $x \mapsto \pi(x)= \mathrm{e}^{-U(x)}/\int_{\mathbb{R}^d} \mathrm{e}^{-U(y)} \mathrm{d} y$.

Bayesian Inference

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